Determine which equation has the same solutions as the given equation. x2 − 10x − 11 = 0

A.
(x − 10)2 = 36
B.
(x − 5)2 = 36
C.
(x − 5)2 = 21
D.
(x − 10)2 = 21

I just want to mention that the question is wrongly written!

it's meant to be  x² − 10x − 11 = 0 and not x2 − 10x − 11 = 0

and so the other equations!

The answer is B: (x − 5)² = 36

Step-by-step explanation:

by solving the equations using the quadratic formula we found:

the solutions for x² − 10x − 11 = 0 | x = 11, -1

the solutions for A | x = 16, 4

the solutions for B | x = 11, -1

the solutions for C | x = ,

the solutions for D | x =

the given equation: x² − 10x − 11 = 0 and the equation B: (x − 5)² = 36 have the same solutions

Therfore B is the correct answer

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

correct

step-by-step explanation: